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Clifford Algebra to Geometric Calculus: A Unified Language for Mathematics and Physics

- D. Hestenes, G. Sobczyk, J. S. Marsh
- Mathematics
- 30 June 1984

1 / Geometric Algebra.- 1-1. Axioms, Definitions and Identities.- 1-2. Vector Spaces, Pseudoscalars and Projections.- 1-3. Frames and Matrices.- 1-4. Alternating Forms and Determinants.- 1-5.… Expand

The Hyperbolic Number Plane

- G. Sobczyk
- Mathematics
- 1 September 1995

INTRODUCTION. The complex numbers were grudgingly accepted by Renaissance mathematicians because of their utility in solving the cubic equation. Whereas the complex numbers were discovered primarily… Expand

Geometric Algebra with Applications in Science and Engineering

- Eduardo Bayro Corrochano, G. Sobczyk
- Mathematics
- 21 October 2012

Advances in Geometric Algebra Computing Lie Algebras and Geometric Algebra, Geometric Filtering, Interpolation, Optimization Geometric Algebra of Computer Vision Neural and Quatum Computing Geometric… Expand

Simplicial calculus with Geometric Algebra

- G. Sobczyk
- Mathematics
- 1992

We construct geometric calculus on an oriented k-surface embedded in Euclidean space by utilizing the notion of an oriented k-surface as the limit set of a sequence of k-chains. This method provides… Expand

Relativity in Clifford's Geometric Algebras of Space and Spacetime

- W. E. Baylis, G. Sobczyk
- Physics, Mathematics
- 7 May 2004

Of the various formalisms developed to treat relativistic phenomena, those based on Clifford's geometric algebra are especially well adapted for clear geometric interpretations and computational… Expand

Lectures on Clifford (geometric) algebras and applications

- R. Ablamowicz, G. Sobczyk
- Mathematics
- 2004

Preface (Rafal Ablamowicz and Garret Sobczyk) * Lecture 1: Introduction to Clifford Algebras (Pertti Lounesto) * 1.1 Introduction * 1.2 Clifford algebra of the Euclidean plane * 1.3 Quaternions * 1.4… Expand

Hybrid Matrix Geometric Algebra

- G. Sobczyk, G. Erlebacher
- Mathematics, Computer Science
- IWMM/GIAE
- 19 May 2004

TLDR

Clifford Geometric Algebras in Multilinear Algebra and Non-Euclidean Geometries

- G. Sobczyk
- Mathematics
- 2004

Given a quadratic form on a vector space, the geometric algebra of the corresponding pseudo-euclidean space is defined in terms of a simple set of rules which characterizes the geometric product of… Expand

Conformal Mappings in Geometric Algebra

- G. Sobczyk
- Mathematics
- 1 February 2012

I n 1878 William Kingdon Clifford wrote down the rules for his geometric algebra, also known as Clifford algebra. We argue in this paper that in doing so he laid down the groundwork that is… Expand

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